There is no evidence from before 200 C.E. of a week that is divorced from the lunar cycle.
A couple years ago, before I started keeping the seventh day sabbath, I studied the Lunar Sabbath. I find the idea very attractive. But one little detail derailed it. The Omer Count, by which you determine Pentecost. I couldn't see any way to count 50 days from a sabbath and end up at the day after another sabbath, if you were using the lunar sabbath system. Yet this is how I thought Pentecost was to be calculated. So I set it aside for a while. Last night I sat down and read an an article called Philo and the Lunar Sabbath, published by Hope of Israel Ministries.
My eyes were opened. Philo was a Jew who was mainstream, orthodox, and accepted by his fellow Jews as a Jew in good standing. Philo lived twenty years before Jesus birth, until twenty years after. So Philo's writings about Judaism of his time apply to the Judaism practiced by Jesus and the Jews around him. Jesus parents fled to Egypt, and would have practiced the lunar sabbath with the Jews in Egypt.
Philo clearly states that the sabbath was counted from the New Moon, as is stated in the Bible. Further, he said that new moon days aren't counted among the days when counting the six days until the seventh day sabbath. If New Moon days aren't counted when you count the Sabbath cycle, then why should you count them when counting the fifty days until Pentecost? For the scriptures say, "number to yourself fifty days, until the morrow after the Sabbath".
Therefore, the only objection I had to the Lunar Sabbath is gone. The fine articles at the Hope of Israel website addressed every other objection I've seen Saturday Sabbath keepers use to preserve their faith. Will I be keeping the Lunar Sabbath? I'll try. And if at some point I find out I'm wrong, I'll stop.
This brings us to the true Pentecost. This morning I found this article, True Pentecost, by Brother Arnold. This article shows from scripture that Pentecost must be 50 days after the seventh sabbath, and not fifty days counting from the first sabbath. If I'd had this understanding from the beginning, the Lunar Sabbath never would have been an issue. Brother Arnold shows that Aaron required three pilgrimages in the first, fourth, and seventh months. If you keep Pentecost in the fourth month, this works out.
I always thought it was odd for Pentecost to come so soon after Passover. If you are busy harvesting, why would you come back to Jerusalem for a festival so quickly, when you just had a big feast at Passover? With the extra fifty days added, it all gets smoothed out. Instead of having a long wait for the feast of Booths, you have Passover, then wait three months, Pentecost, three months, then Tabernacles. This way is smooth, just feels right, and is supported by scripture.
Give the Pentecost article a read; you don't have to believe in Lunar Sabbaths to appreciate the arguments that it makes for a fourth month Pentecost.